Work & Power

1. Work & Power Physics 4th Six Weeks

2. Work • Scientifically speaking, Work is defined as the transfer of energy that occurs when a force makes an object move. • For work to be done, a force must cause something to move. • When work is done, a transfer of energy always occurs. • Energy is always transferred from the object that is doing the work to the object on which the work is done. • You carry a box up a flight of stairs, you transferred energy from your moving muscles to the box and increased its potential energy by increasing its height.

3. WORK • The amount of work depends upon two things: the amount of force exerted and the distance over which the force is applied. • A force at an angle is not as effective at doing work, because only the part of the force in the direction of the motion does work in the physics sense. • Work = Force x Distance • Energy is also defined as “The ability to do Work” • Force is measured in Newtons in the formula, and distance is measured in meters. Work, like energy is measured in Joules. • The Joule is the amount of energy required to apply a force of 1 Newton over a distance of 1 Meter. The Joule is the unit of work. 1 Joule = 1 Newton * 1 meter 1 J = 1 N * m

4. Two things MUST occur for work to be done. 1) The object must move 2) The object must move in the same direction as the force.

5. Circle diagram for the Work formula W F D W = Work F = Force D = Distance

6. Example:A book being lifted off a desk. This IS work because the force is being applied upward AND the books are moving upward.

7. You carrying your lunch to the table. This IS NOT work because the force on your lunch is upward while it is moving horizontally.

8. WORK, continued • It can be accurately noted that the waiter's hand did push forward on the tray for a brief period of time to accelerate it from rest to a final walking speed. • But once up to speed, the tray will stay in its straight-line motion at a constant speed without a forward force. (remember 1st Law) • And if the only force exerted upon the tray during the constant speed stage of its motion is upward, then no work is done upon the tray. • Again, a vertical force does not do work on a horizontally displaced object.

9. Example 1) How much work is performed when a 50 kg crate is pushed 15 m with a force of 20 N? F 300 J G 750 J H 1,000 J J 15,000 J Use the formula Work = Force x distance Force of 20 N x 15 meters = ?? Answer:

10. Example # 2

11. Example # 3 Force Force Force Force

12. The Work-Energy Theorem • The work-energy theorem states that whenever work is done energy changes. • Work = Δ Energy • The kinetic energy of a moving object is equal to the work required to bring it to that speed from rest, or the work the object can do while being brought to rest. • If you threw a baseball, you do work on it to give it speed as it leaves your hand. • The moving ball can then hit something and push it, doing work on what it hits. • For example: the work done to stop a car is friction force x distance of skid, therefore: Fd = ½ mv2

13. The Work-Energy Theorem: Stopping Distance Example so… Fd = ½ mv2 d = A car has a mass of 1500 kg and was driving at a speed of 11 m/s (~ 25 miles per hour). A deer ran in front of the car and the driver slammed on the brakes causing the car to skid to a halt. If the brakes and the tires applied approximately 11000 N (~ 2500 pounds), how far did the car skid? d = d = d = d = d = 8.25 m

14. The Work-Energy Theorem: Stopping Distance Example (twice as fast) so… Fd = ½ mv2 d = A car has a mass of 1500 kg and was driving at a speed of 22 m/s (~ 50 miles per hour). A deer ran in front of the car and the driver slammed on the brakes causing the car to skid to a halt. If the brakes and the tires applied approximately 11000 N (~ 2500 pounds), how far did the car skid? d = d = d = *Note: if the car was going four timesas fast, stopping distance wouldn’t be 4x as far but 16x as far it would be 132 m *Force is the same since that mass covers greater distance at a higher speed. Also the force is the friction force which depends upon the surface & normal (speed doesn’t change those) d = d = 33 m

15. From the STAAR Reference Materials

17. Example Problem #4 A toy train moving down a track has 60 J of KE at point A and at point B it is slowing down and has 30 J of KE. How much work is done in slowing the toy train down? W = ∆KE = KEf – KEi W = 30 J – 60 J W = - 30 J

18. 1000J /60 sec=16.67W Power 1000J/10sec =100W • Power is defined as the amount of work done in a certain amount of time. • Power is also known as the rate at which work is done. • A more powerful machine does the same amount of work in less time than a less powerful one • Power is measured in Watts (W). • 1 W = 1J/second • A Watt is small, it is about the amount of energy required to raise a glass of water from a table to your mouth in 1 second.

19. Power, continued • A common English unit for Power is the horsepower (hp) • 1 horsepower = 746 Watts and was originally thought to be the average power output of a horse. • James Watt thought a horse • Could do 33,000 ft-lbs of work • per minute (550 ft-lbs/sec) • For example, a horse exerting • 1 horsepower can raise 330 lbs • Of coal 100 feet in 1 minute. • You can make up whatever • combination of feet and pounds • you like. As long as the product is • 33,000 foot-pounds in one minute, you have a horsepower.

20. POWER FORMULAS • Because the watt is so small, large amounts of power are often expressed in Kilowatts (kW). 1 kW = 1000 W. • Energy can be transferred in ways that don’t require work being done as well. For example a light bulb uses energy to produce light and heat, but no work is being done. • So…Power is also the amount of energy transferred to an object in a period of time. • Therefore… a 100 W light bulb uses energy at a rate of 100 J/s.

21. Circle Diagrams for the Power formulas E W P P T T P = Power W = Work T = Time E = Energy

22. Review: work & power If a force of 100 Newtons was exerted on an object and no work was done, the object must have — A. accelerated rapidly B. remained motionless C. decreased its velocity D. gained momentum

23. Review: work & power A horizontal force of 600 N is used to push a box 8 m across a room. Which of these variables must be known to determine the power used in moving the box? A. The weight of the box B. The potential energy of the box C. The time it takes to move the box D. The length of the box

24. Review: work & power The weight lifter used a force of 980. N to raise the barbell over her head in 5.21 seconds. Approximately how much work did she do in raising the barbell? W = Fd = 980.0 N (2.040 m) = Example 4: How much power did she have? P = W / t = 1999.2 J / 5.21 s P = 1999 J 384 W

25. Example # 5 Work Work Work x 10 sec Work

26. Example # 6 Time Time Time Time Time Time

27. Torque • Torque is a measure of how much a force acting on an object causes that object to rotate • The object rotates about an axis, which we call the pivot point

28. Torque, continued The Greek letter tau Example: T = 0.24 m x 50 N T = 12 N ·m • Since torque is the product of a force that is perpendicular to the distance it is applied, while Work is the product of a force that is parallel to the direction of the force that is applied, different units are used: • Joules for Work • N-m for Torque • Note: the English unit for Torque is the “foot-pound”

29. Circle diagram for the Torque formula r = F r = Torque F = Force r = Lever Arm

30. Torque Example 2: A torque of 500 N-m is applied to a handle. The force is applied 0.5 m from the pivot point. What is the force?

31. Torque Example 3: